A film which a large number of a layer having a low refractive index and a layer having a high refractive index are alternately laminated can be formed into an optical interference film which selectively reflects or transmits a light having a specific wavelength due to structural optical interference between the layers. In addition, such a multi-layer laminate film is able to obtain a high reflection comparable to a film using a metal by gradually changing the film thickness or stacking a film having a different reflection peak and can also be used as a metal luster film or a reflection mirror. Furthermore, by stretching such a multi-layer laminate film to only one direction, the stretched film can reflect only a specific polarization component, whereas it is able to transmit a polarization component in the orthogonal direction thereto, and it can be used as a polarization reflection film. Therefore, such a multi-layer laminate film is used as a brightness enhancing film for liquid crystal displays or the like.
In general, in a multi-layer optical film constituted of layers having a layer thickness of 0.05 to 0.5 μm and having a different refractive index from each other, there is found a phenomenon of increased reflection in which a light having a specific wavelength is reflected due to a difference in refractive index between a layer constituting a one-sided layer and a layer constituting the other-sided layer, the film thickness, and the number of layers. In general, its reflection wavelength is expressed according to the following equation.λ=2(n1×d1+n2×d2)
(In the foregoing equation, λ represents a reflection wavelength (nm); n1 and n2 represent refractive indices of the layers, respectively; and d1 and d2 represent thicknesses (nm) of the layers, respectively.)
For example, as shown in Patent Document 1, only a specific polarization component can be reflected by a method in which by using a resin having a positive stress optical coefficient in a one-sided layer, a refractive index of such a layer is made birefringent by means of uniaxial stretching to bring anisotropy, thereby making a difference in refractive index between the layers in the stretching direction within the film plane large and meanwhile making a difference in refractive index between the layers in the orthogonal direction to the stretching direction within the film plane small.
By utilizing this principle, for example, it is possible to design a reflection polarization film which reflects a polarized light in one direction and transmits a polarized light in the orthogonal direction thereto. At that time, desired birefringency is expressed according to the following equations.n1x>n2x, ny=n2y 
(In the foregoing equations, n1x and n2x represent refractive indices in the stretching direction in the layers, respectively; and ny and n2y represent refractive indices in the orthogonal direction to the stretching direction in the layers, respectively.)
In addition, in Patent Document 2, a multi-layer film in which polyethylene-2,6-naphthalene dicarboxylate (hereinafter sometimes referred to as “2,6-PEN”) is used in a layer having a high refractive index, and PEN copolymerized with 30 mol % of a thermoplastic elastomer or terephthalic acid is used in a layer having a low refractive index is exemplified. This exemplifies a reflection polarization film which reflects only a specific polarized light by using a resin having a positive stress optical coefficient in a one-sided layer and using a resin having a very small stress optical coefficient (revelation of birefringence by stretching is extremely small) in the other-sided layer.
Investigations regarding such a reflection polarization film are to pay attention to mainly a difference in refractive index between the layers in the stretching direction and a difference in refractive index between the layers in the orthogonal direction to the stretching direction within the film plane and to reflect a polarized light which does not transmit toward the light source side to reuse the light, thereby increasing the brightness enhancing performance.
Meanwhile, with respect to techniques paying attention to reuse of a polarization component which does not transmit, a reflectance of the polarization component reaches the vicinity of 100%, and therefore, it is the state that it is difficult to further enhance the brightness enhancing performance by merely the method of reusing such a polarized light.
In addition, in Patent Document 3, though a uniaxially stretched multi-layer laminate film in which polyethylene-2,6-naphthalene dicarboxylate and syndiotactic polystyrene are alternately laminated is disclosed, it is concerned with the reflection at only a certain part of wavelength peak and has a high transmittance as a film, but it does not propose a concept of brightness enhancing film.
(Patent Document 1) JP-A-04-268505
(Patent Document 2) JP-T-9-506837
(Patent Document 3) WO01/47711